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🇵🇰 NED Admission Test · flashcards
NED Admission Test Mathematics Flashcards
69 question-and-answer cards covering Mathematics as it is examined in NED Admission Test. 24 of them are printed below, taken from across the deck — no signup, no paywall on the preview.
24 sample cards from the Mathematics deck
Sampled from the end of the deck, so these are different cards from the ones shown on the syllabus page.
What is the adjoint (adjugate) of a matrix?
The transpose of the matrix of cofactors of A.
Give the inverse of a 2×2 matrix A = [[a, b],[c, d]].
A⁻¹ = (1/(ad − bc)) · [[d, −b],[−c, a]], provided ad − bc ≠ 0.
What is the defining property of the inverse A⁻¹ of a matrix A?
AA⁻¹ = A⁻¹A = I, the identity matrix.
State Cramer's Rule condition for a unique solution of a linear system AX = B.
A unique solution exists if and only if the coefficient determinant |A| ≠ 0, and then xᵢ = |Aᵢ| / |A|.
In the matrix method, how is the solution of the system AX = B found?
By X = A⁻¹B, provided A is non-singular (|A| ≠ 0).
What is an arithmetic progression (A.P.)?
A sequence in which each term after the first is obtained by adding a fixed number (the common difference d) to the preceding term.
What is the formula for the nth term of an A.P. with first term a and common difference d?
aₙ = a + (n − 1)d.
What is the sum of the first n terms of an A.P.?
Sₙ = (n/2)[2a + (n − 1)d] = (n/2)(a + l), where l is the last term.
What is a geometric progression (G.P.)?
A sequence in which each term after the first is obtained by multiplying the preceding term by a fixed non-zero number (the common ratio r).
What is the formula for the nth term of a G.P. with first term a and common ratio r?
aₙ = a·rⁿ⁻¹.
What is the sum of the first n terms of a G.P. (r ≠ 1)?
Sₙ = a(rⁿ − 1)/(r − 1) = a(1 − rⁿ)/(1 − r).
What is the sum to infinity of a G.P., and when does it exist?
S∞ = a/(1 − r), valid only when |r| < 1.
What is a harmonic progression (H.P.)?
A sequence whose reciprocals form an arithmetic progression; e.g. 1/a, 1/(a+d), 1/(a+2d), ...
How do you find the nth term of a harmonic progression?
Take the corresponding A.P. of the reciprocals, find its nth term using a + (n−1)d, then take the reciprocal of that result.
What is the arithmetic mean (A.M.) of two numbers a and b?
A.M. = (a + b)/2.
What is the geometric mean (G.M.) of two positive numbers a and b?
G.M. = √(ab).
What is the harmonic mean (H.M.) of two non-zero numbers a and b?
H.M. = 2ab/(a + b).
State the relationship between A.M., G.M. and H.M. of two positive numbers.
G.M.² = A.M. × H.M., and they satisfy A.M. ≥ G.M. ≥ H.M. (equality when the numbers are equal).
How do you insert n arithmetic means between two numbers a and b?
Form an A.P. with a as first term and b as the (n+2)th term; the common difference is d = (b − a)/(n + 1), giving the means a + d, a + 2d, ..., a + nd.
How do you insert a single geometric mean G between two positive numbers a and b?
G = √(ab), since a, G, b form a G.P. with G/a = b/G.
If a, b, c are in A.P., what relation holds among them?
2b = a + c (the middle term is the arithmetic mean of the other two).
If a, b, c are in G.P., what relation holds among them?
b² = ac (the middle term is the geometric mean of the other two).
If a, b, c are in H.P., what relation holds among them?
b = 2ac/(a + c), i.e. 1/a, 1/b, 1/c are in A.P. so 2/b = 1/a + 1/c.
What is the cofactor of an element aᵢⱼ in a determinant?
Cᵢⱼ = (−1)^(i+j) · Mᵢⱼ, where Mᵢⱼ is the minor of aᵢⱼ (the determinant left after deleting row i and column j).
What this deck covers
The Mathematics deck follows the NED Admission Test Mathematics syllabus — 12 chapters and 49 topics — so questions land on material that is genuinely examinable rather than trivia around it. That works out to roughly 5.8 cards per chapter.
Answers are written to be recallable, not just readable — averaging about 68 characters, which is long enough to carry the reasoning and short enough to say out loud.
A deck like this earns its keep on the second and third pass. Read the syllabus first so you know the shape of the subject, then use the cards to find the specific facts that have not stuck.
Mathematics flashcards FAQ
How many Mathematics flashcards are in this NED Admission Test deck?
69 cards. This page previews 24 of them, sampled evenly across the deck so you can judge the difficulty before installing anything.
Are these NED Admission Test flashcards free?
Yes. The preview here is free to read with no signup, and the full 69-card deck is free inside the Examius app.
What do the Mathematics cards cover?
They follow the NED Admission Test Mathematics syllabus — 12 chapters and 49 topics — so the questions track what is actually examinable.
How should I use these flashcards?
Read the syllabus first so you know the shape of the subject, then drill the deck. Examius schedules each card with spaced repetition, so cards you keep missing come back sooner and ones you know drift further apart.